From molecular dynamics to kinetic theory and hydrodynamics

Thierry Bodineau; Isabelle Gallagher; Laure Saint-Raymond

From molecular dynamics to kinetic theory and hydrodynamics

Thierry Bodineau
, Isabelle Gallagher
, Laure Saint-Raymond

École Polytechnique

Laboratoire de Probabilités et Modèles Aléatoires
Département de Mathématiques et Applications
Sorbonne Université

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › peer-review

Abstract

In these notes we present the main ingredients of the proof of the convergence of the distribution function of a tagged particle in a background initially at equilibrium, towards the solution to the heat equation. We also show how the process associated with the tagged particle converges in law towards a Brownian motion.

Original language	English
Title of host publication	Invited Lectures
Editors	Sun Young Jang, Young Rock Kim, Dae-Woong Lee, Ikkwon Yie
Publisher	KYUNG MOON SA Co. Ltd.
Pages	721-746
Number of pages	26
ISBN (Electronic)	9788961058063
Publication status	Published - 1 Jan 2014
Event	2014 International Congress of Mathematicans, ICM 2014 - Seoul, Korea, Republic of Duration: 13 Aug 2014 → 21 Aug 2014

Publication series

Name	Proceeding of the International Congress of Mathematicans, ICM 2014
Volume	3

Conference

Conference	2014 International Congress of Mathematicans, ICM 2014
Country/Territory	Korea, Republic of
City	Seoul
Period	13/08/14 → 21/08/14

Keywords

BBGKY hierarchy
Boltzmann equation
Branching process
Brownian motion
Heat equation
Low density limit

Cite this

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title = "From molecular dynamics to kinetic theory and hydrodynamics",

abstract = "In these notes we present the main ingredients of the proof of the convergence of the distribution function of a tagged particle in a background initially at equilibrium, towards the solution to the heat equation. We also show how the process associated with the tagged particle converges in law towards a Brownian motion.",

keywords = "BBGKY hierarchy, Boltzmann equation, Branching process, Brownian motion, Heat equation, Low density limit",

author = "Thierry Bodineau and Isabelle Gallagher and Laure Saint-Raymond",

year = "2014",

month = jan,

day = "1",

language = "English",

series = "Proceeding of the International Congress of Mathematicans, ICM 2014",

publisher = "KYUNG MOON SA Co. Ltd.",

pages = "721--746",

editor = "Jang, \{Sun Young\} and Kim, \{Young Rock\} and Dae-Woong Lee and Ikkwon Yie",

booktitle = "Invited Lectures",

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Bodineau, T, Gallagher, I & Saint-Raymond, L 2014, From molecular dynamics to kinetic theory and hydrodynamics. in SY Jang, YR Kim, D-W Lee & I Yie (eds), Invited Lectures. Proceeding of the International Congress of Mathematicans, ICM 2014, vol. 3, KYUNG MOON SA Co. Ltd., pp. 721-746, 2014 International Congress of Mathematicans, ICM 2014, Seoul, Korea, Republic of, 13/08/14.

From molecular dynamics to kinetic theory and hydrodynamics. / Bodineau, Thierry; Gallagher, Isabelle; Saint-Raymond, Laure.
Invited Lectures. ed. / Sun Young Jang; Young Rock Kim; Dae-Woong Lee; Ikkwon Yie. KYUNG MOON SA Co. Ltd., 2014. p. 721-746 (Proceeding of the International Congress of Mathematicans, ICM 2014; Vol. 3).

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › peer-review

TY - GEN

T1 - From molecular dynamics to kinetic theory and hydrodynamics

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AU - Gallagher, Isabelle

AU - Saint-Raymond, Laure

PY - 2014/1/1

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N2 - In these notes we present the main ingredients of the proof of the convergence of the distribution function of a tagged particle in a background initially at equilibrium, towards the solution to the heat equation. We also show how the process associated with the tagged particle converges in law towards a Brownian motion.

AB - In these notes we present the main ingredients of the proof of the convergence of the distribution function of a tagged particle in a background initially at equilibrium, towards the solution to the heat equation. We also show how the process associated with the tagged particle converges in law towards a Brownian motion.

KW - BBGKY hierarchy

KW - Boltzmann equation

KW - Branching process

KW - Brownian motion

KW - Heat equation

KW - Low density limit

M3 - Conference contribution

AN - SCOPUS:85086716423

T3 - Proceeding of the International Congress of Mathematicans, ICM 2014

SP - 721

EP - 746

BT - Invited Lectures

A2 - Jang, Sun Young

A2 - Kim, Young Rock

A2 - Lee, Dae-Woong

A2 - Yie, Ikkwon

PB - KYUNG MOON SA Co. Ltd.

T2 - 2014 International Congress of Mathematicans, ICM 2014

Y2 - 13 August 2014 through 21 August 2014

ER -

From molecular dynamics to kinetic theory and hydrodynamics

Abstract

Publication series

Conference

Keywords

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Cite this